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The equation [tex]F = \frac{9}{5} C + 32[/tex] gives the relationship between temperatures measured in degrees Celsius and degrees Fahrenheit.

Use an inequality to represent the corresponding Celsius temperature that is at or below [tex]59^{\circ} F[/tex].

Answer :

To find the corresponding Celsius temperature that is at or below [tex]\(59^\circ F\)[/tex], we can use the given equation:

[tex]\[ F = \frac{9}{5}C + 32 \][/tex]

We're given that the Fahrenheit temperature [tex]\(F\)[/tex] is at or below [tex]\(59^\circ F\)[/tex]. So, we set up the inequality:

[tex]\[ \frac{9}{5}C + 32 \leq 59 \][/tex]

Now, we need to solve this inequality for [tex]\(C\)[/tex]:

1. Subtract 32 from both sides to isolate the term with [tex]\(C\)[/tex] on one side:

[tex]\[ \frac{9}{5}C \leq 59 - 32 \][/tex]

[tex]\[ \frac{9}{5}C \leq 27 \][/tex]

2. Multiply both sides by the reciprocal of [tex]\(\frac{9}{5}\)[/tex], which is [tex]\(\frac{5}{9}\)[/tex], to solve for [tex]\(C\)[/tex]:

[tex]\[ C \leq 27 \times \frac{5}{9} \][/tex]

[tex]\[ C \leq 15 \][/tex]

Thus, the Celsius temperature corresponding to or below [tex]\(59^\circ F\)[/tex] is [tex]\(15^\circ C\)[/tex].

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